Uncertainty In Parameter Estimates Research Articles

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

Identifiability investigation of within-host models of acute virus infection

<p>Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we used four mathematical models of influenza A infection with increased degrees of biological realism. We tested the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refined the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we presented insight into the sources of uncertainty in parameter estimation and provided guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.</p>

Marginal Percentile Intervals in Bayesian Inference are Overconfident

In Bayesian statistics, Highest Posterior Density Regions (HPDR) measure the uncertainty of parameter estimates at a given credibility level. HPDRs are the Bayesian version of Highest Density Intervals (HDI) based on the posterior probability. The calculation of Percentile Intervals (PI) is a common method for approximating HDIs in many popular Python toolboxes. The PI calculation differs from the HPDR calculation as it ignores the posterior probability by simply cutting the lower and upper values of the marginalized posterior distribution symmetrically. Here, we use the phenomenological retarded transient functions to infer the posterior distribution of a clinical dataset. The one-dimensional HPDR projections were compared to the PIs for all inferred parameters. The direct comparison revealed that the one-dimensional HPDR projections of all inferred parameter posteriors exceeded the percentile-based intervals, demonstrating that the PIs were overconfident. Overall, we argue that only HPDRs can be interpreted in terms of probability.

Multistatic radar distribution geometry effects on parameter estimation accuracy

AbstractAn analysis of the parameter estimation uncertainty for the target location and velocity achievable using a single‐transmitter‐multiple‐receiver multistatic radar system is presented. A framework for establishing measures of multistatic radar parameter uncertainties by expansion of the bistatic radar parameter uncertainty measures is presented for systems containing omnidirectionally radiating nodes. The methodology uses analytical methods based on the Cramér–Rao Lower Bounds applied to scenarios in a two‐dimensional physical space with a single target exhibiting Doppler characteristics and a bistatic angle dependent radar cross‐section. A set of geometric descriptors is proposed to characterise the system, and parameter uncertainty results are reported as a function of these descriptors. The results indicate that angular separation between the transmitter and the centre of the receiver distribution is of greater importance than the quantity of receivers within the system when low uncertainty estimation capabilities are desired, though a minimum of two receivers must be available. The proportion of receivers within the system which contributed information crucial to obtaining the minimum estimation uncertainty is reported for systems containing different quantities of receivers. It was observed that, as the total number of receivers available increased, the proportion of receivers required to achieve the minimal uncertainty level reduces significantly.

Modelling the population-level benefits and cost-effectiveness of cell-based quadrivalent influenza vaccine for children and adolescents aged 6 months to 17 years in the US

ABSTRACT Background Cell-based quadrivalent influenza vaccines (QIVc) can increase effectiveness against seasonal influenza by avoiding mismatch from egg adaption of vaccine viruses. This study evaluates the population-level cost-effectiveness and impacts on health outcomes of QIVc versus an egg-based vaccine (QIVe) in children aged 6 months to 17 years in the US. Research Design and Methods A dynamic age-structured susceptible-exposed-infected-recovered model was used to simulate influenza transmission in low and high incidence seasons for two scenarios: 1. QIVe for 6 months–17 year-olds, QIVc for 18–64 year-olds, and adjuvanted QIV (aQIV) for ≥ 65 year-olds, and 2. QIVc for 6 months–64 year-olds, and aQIV for ≥ 65 year-olds. Probabilistic sensitivity analysis was performed to account for uncertainty in parameter estimates. Cost-effectiveness was evaluated as incremental cost-effectiveness ratios (ICERs). Results Extension of QIVc to children resulted in 3–4% reductions in cases (1,656,271), hospitalizations (16,688), and deaths (2,126) at a population level in a high incidence season, and 65% reductions (cases: 2,856,384; hospitalizations: 31667; deaths: 4,163) in a low incidence season. Use of QIVc would be cost-saving, with ICERs of -$16,427/QALY and -$8,100/QALY from a payer perspective and -$22,669/QALY and -$15,015/QALY from a societal perspective, for low and high incidence seasons respectively. Cost savings were estimated at approximately $468 million and $1.366 billion for high and low incidence seasons, respectively. Conclusion Use of QIVc instead of QIVe in children > 6 months of age in the US would reduce the disease burden and be cost-saving from both a payer and societal perspective.

Using Bayesian Neural Networks to Select Features and Compute Credible Intervals for Personalized Survival Prediction.

An Individual Survival Distribution (ISD) models a patient's personalized survival probability at all future time points. Previously, ISD models have been shown to produce accurate and personalized survival estimates (for example, time to relapse or to death) in several clinical applications. However, off-the-shelf neural-network-based ISD models are usually opaque models due to their limited support for meaningful feature selection and uncertainty estimation, which hinders their wide clinical adoption. Here, we introduce a Bayesian-neural-network-based ISD (BNN-ISD) model that produces accurate survival estimates but also quantifies the uncertainty in model's parameter estimation, which can be used to (1) rank the importance of the input features to support feature selection and (2) compute credible intervals around ISDs for clinicians to assess the model's confidence in its prediction. Our BNN-ISD model utilized sparsity-inducing priors to learn a sparse set of weights to enable feature selection. We provide empirical evidence, on 2 synthetic and 3 real-world clinical datasets, that BNN-ISD system can effectively select meaningful features and compute trustworthy credible intervals of the survival distribution for each patient. We observed that our approach accurately recovers feature importance in the synthetic datasets and selects meaningful features for the real-world clinical data as well, while also achieving state-of-the-art survival prediction performance. We also show that these credible regions can aid in clinical decision-making by providing a gauge of the uncertainty of the estimated ISD curves.

Using Auxiliary Item Information in the Item Parameter Estimation of a Graded Response Model for a Small to Medium Sample Size: Empirical Versus Hierarchical Bayes Estimation.

Marginal maximum likelihood estimation (MMLE) is commonly used for item response theory item parameter estimation. However, sufficiently large sample sizes are not always possible when studying rare populations. In this paper, empirical Bayes and hierarchical Bayes are presented as alternatives to MMLE in small sample sizes, using auxiliary item information to estimate the item parameters of a graded response model with higher accuracy. Empirical Bayes and hierarchical Bayes methods are compared with MMLE to determine under what conditions these Bayes methods can outperform MMLE, and to determine if hierarchical Bayes can act as an acceptable alternative to MMLE in conditions where MMLE is unable to converge. In addition, empirical Bayes and hierarchical Bayes methods are compared to show how hierarchical Bayes can result in estimates of posterior variance with greater accuracy than empirical Bayes by acknowledging the uncertainty of item parameter estimates. The proposed methods were evaluated via a simulation study. Simulation results showed that hierarchical Bayes methods can be acceptable alternatives to MMLE under various testing conditions, and we provide a guideline to indicate which methods would be recommended in different research situations. R functions are provided to implement these proposed methods.

Improving the statistical reliability of river model predictions via simple state adjustments

A major challenge in hydrologic modelling is producing reliable uncertainty estimates outside of calibration periods. One obvious strategy is to improve model structures utilising advancements in process knowledge and observations. Another statistically relevant approach is to develop improved error models so that the uncertainty can be more reliably estimated. The recently introduced river bed/bank storage (RBS) model is an improved representation of transmission losses/gains within basin-scale river system models. The novelty of the current research is the way the RBS model is combined with State and Parameter Uncertainty Estimation (SPUE) to produce more statistically reliable predictions. Using the RBS model with SPUE resulted in better matched predictive distributions in 13 out of 16 test cases, and higher proportions of observed values within the predictive ranges for all cases. The paper demonstrates that improving model structures combined with better characterisation of state error can alleviate issues of overfitting in predictions.

Soilfoodwebs: An R package for analyzing and simulating nutrient fluxes through food webs

Soil food web models can calculate the fluxes of carbon and nitrogen between soil organisms and so estimate the impact of individual organisms on ecosystem processes. These modelling approaches go beyond standard techniques in ecology. So, an open-source tool supporting them along with an analysis of their strengths and weaknesses could help. We present the R package soilfoodwebs, which calculates carbon and nitrogen fluxes through food webs and contributes four new features that are documented in the literature but unavailable in open-source software: (1) diet and physiological rates that balance multiple chemical elements, (2) estimates of parameter and structural uncertainty, (3) estimates of direct and indirect effects of taxa on ecosystem processes, and (4) a conversion from equilibrium food web analyses to simulations that can estimate the response to change. soilfoodwebs balances carbon and nitrogen demand by adjusting each organism's diet and the efficiency with which they use carbon. We outline the theory behind the package and demonstrate its functions using soil food web models available in the literature. Our analysis shows that the calculation of fluxes and the contributions of individual taxa to mineralization or decomposition rates is the strength of the soilfoodwebs package and soil food web models. We also show that more detailed information on population regulation (i.e., density-dependence) is needed for using these models to predict trends over time. Outputs from soil food web models can be compared with ecosystem measurements (e.g., mineralization, decomposition) and guide empirical work towards functionally important and undocumented soil biodiversity.

Global Temperature Projections from a Statistical Energy Balance Model Using Multiple Sources of Historical Data

Abstract This paper estimates a two-component energy balance model as a linear state-space system (EBM-SS model) using historical data. It is a joint model for the temperature in the mixed layer, the temperature in the deep ocean layer, and radiative forcing. The EBM-SS model allows for the modeling of nonstationarity in forcing and the incorporation of multiple data sources for the unobserved processes. We estimate the EBM-SS model using historical datasets at the global level for the period 1955–2020 by maximum likelihood. We show in the empirical estimation and in simulations that using multiple data sources for the unobserved processes reduces parameter estimation uncertainty. When fitting the EBM-SS model to six observational global mean surface temperature (GMST) anomaly series, the GMST projections under representative concentration pathway scenarios are comparable to those from Coupled Model Intercomparison Project models. The results show that a simple statistical climate model estimated on the historical period can produce GMST projections compatible with output from large-scale Earth system models. Significance Statement We develop a statistical model to understand Earth’s energy balance and how it impacts temperature across the planet’s surface and deep oceans. Unlike previous approaches, ours is fully statistical. This means that we use maximum likelihood to calculate the estimates and evaluate the level of uncertainty in the model’s parameters. By applying the model to historical data from 1955 to 2020, we are able to make predictions about the average global surface temperature that are consistent with those from the Coupled Model Intercomparison Project. Our findings support current predictions about global temperatures using a straightforward statistical climate model, grounded in historical data.

(N)NLO+NLL’ accurate predictions for plain and groomed 1-jettiness in neutral current DIS

The possibility to reanalyse data taken by the HERA experiments offers the chance to study modern QCD jet and event-shape observables in deep-inelastic scattering. To address this, we compute resummed and matched predictions for the 1-jettiness distribution in neutral current DIS with and without grooming the hadronic final state using the soft-drop technique. Our theoretical predictions also account for non-perturbative corrections from hadronisation through parton-to-hadron level transfer matrices extracted from dedicated Monte Carlo simulations with Sherpa. To estimate parameter uncertainties in particular for the beam-fragmentation modelling we derive a family of replica tunes to data from the HERA experiments. While NNLO QCD normalisation corrections to the NLO+NLL’ prediction are numerically small, hadronisation corrections turn out to be quite sizeable. However, soft-drop grooming significantly reduces the impact of non-perturbative contributions. We supplement our study with hadron-level predictions from Sherpa based on the matching of NLO QCD matrix elements with the parton shower. Good agreement between the predictions from the two calculational methods is observed.

Adaptive economic predictive control for offshore wind farm active yaw considering generation uncertainty

Inevitable model uncertainty could render active yaw control (AYC) to make suboptimal or even irrational decisions. To this end, this paper quantitatively analyzes the influential mechanisms of uncertainty on optimal yaw policy in terms of the wake model and power model. In order to address power model uncertainty that has received little attention in the AYC field, this paper proposes an efficient adaptive economic predictive control. This framework begins with the construction of a neural network-based compensator to provide online adaptive estimation of parameter uncertainty. On this basis, an adaptive economic predictive control with the economic objective of maximizing the total power is designed to increase the confidence of yaw policy in the presence of generation uncertainty, and a parallel heuristic solver is developed to allow real-time control of large-scale wind farms. Finally, extensive results based on three wind farm cases demonstrate the effectiveness and advantages of the proposed control strategy.

An uncertainty quantification framework for logistic regression based geospatial natural hazard modeling

There is a class of data-driven global natural hazard predictive models that take advantage of broadly available geospatial proxies. These data-driven geospatial models have been commonly used for landslides and are becoming more available in recent years for liquefaction. Logistic regression is the most common method for predicting these ground failure occurrences. These models do not often include robust quantification of uncertainties although they are widely used in the pre-disaster planning and post-disaster response around the world. Taking the logistic regression based global geospatial liquefaction model (GGLM) (Zhu et al., 2017) as an example, we propose an uncertainty quantification (UQ) framework that consists of characterization of different sources of uncertainty, model sensitivity analysis, and forward uncertainty propagation. In this study, we have identified the main sources of uncertainty in such predictive models as parameter estimation uncertainty, modeling error, and geospatial input uncertainty. A Bayesian inference algorithm is used to quantify the posterior distribution of model parameters and quantify model parameter estimation uncertainties which are found to be negligible when a large amount of data is used in the parameter estimation process. Modeling errors are characterized based on the observed residuals between model predictions and measurements and by fitting a Gaussian distribution to the liquefaction probability residuals. The geospatial input uncertainties are characterized using the literature and expert judgment and propagated into model output. Second, we investigate the sensitivity of model output to different uncertain inputs and find that the variance of model output is largely controlled by the geospatial input uncertainties and model errors. Last, we propose an approximate forward uncertainty propagation method, which provides comparable results to a Monte Carlo simulation-based method with better computational efficiency. The proposed UQ framework provides a measure of uncertainty on model predictions and can be applied to any logistic-regression models and other geospatial modeling problems.

Uniformly valid inference based on the Lasso in linear mixed models

Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics, and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are based on Lasso-type estimators. Aside from providing confidence regions, this also allows for quantification of the joint uncertainty of both variable selection and parameter estimation in the procedure. To show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter spaces of both the regression coefficients and the covariance parameters, we also prove the novel result on uniform Cramér consistency of the restricted maximum likelihood (REML) estimators of the covariance parameters. The superiority of the constructed confidence sets to naïve post-selection procedures is validated in simulations and illustrated with a study of the acid-neutralization capacity of lakes in the United States.

The Effect of Historical Data-Based Informative Prior on Benchmark Dose Estimation of Toxicogenomics.

High-throughput toxicogenomics as an advanced toolbox of Tox21 plays an increasingly important role in facilitating the toxicity assessment of environmental chemicals. However, toxicogenomic dose-response analyses are typically challenged by limited data, which may result in significant uncertainties in parameter and benchmark dose (BMD) estimation. Integrating historical data via prior distribution using a Bayesian method is a useful but not-well-studied strategy. The objective of this study is to evaluate the effectiveness of informative priors in genomic dose-response modeling and BMD estimation. Specifically, we aim to identify plausible informative priors and evaluate their effects on BMD estimates at both gene and pathway levels. A general informative prior and eight time-specific (from 3 h to 29 d) informative priors for seven commonly used continuous dose-response models were derived. Results suggest that the derived informative priors are sensitive to the specific data sets used for elicitation. Real data-based simulations indicate that BMD estimation with the time-specific informative priors can achieve increased or equivalent accuracy, significantly decreased uncertainty, and a slightly enhanced correlation with the points of departure estimated from apical end points than the counterparts with noninformative priors. Overall, our study systematically examined the effects of historical data-based informative priors on BMD estimates, highlighting the benefits of plausible information priors in advancing the practice of toxicogenomics.

Listening efficiency in adult cochlear-implant users compared with normally-hearing controls at ecologically relevant signal-to-noise ratios.

Due to having to work with an impoverished auditory signal, cochlear-implant (CI) users may experience reduced speech intelligibility and/or increased listening effort in real-world listening situations, compared to their normally-hearing (NH) peers. These two challenges to perception may be usefully integrated in a measure of listening efficiency: conceptually, the amount of accuracy achieved for a certain amount of effort expended. We describe a novel approach to quantifying listening efficiency based on the rate of evidence accumulation toward a correct response in a linear ballistic accumulator (LBA) model of choice decision-making. Estimation of this objective measure within a hierarchical Bayesian framework confers further benefits, including full quantification of uncertainty in parameter estimates. We applied this approach to examine the speech-in-noise performance of a group of 24 CI users (M age: 60.3, range: 20-84 years) and a group of 25 approximately age-matched NH controls (M age: 55.8, range: 20-79 years). In a laboratory experiment, participants listened to reverberant target sentences in cafeteria noise at ecologically relevant signal-to-noise ratios (SNRs) of +20, +10, and +4 dB SNR. Individual differences in cognition and self-reported listening experiences were also characterised by means of cognitive tests and hearing questionnaires. At the group level, the CI group showed much lower listening efficiency than the NH group, even in favourable acoustic conditions. At the individual level, within the CI group (but not the NH group), higher listening efficiency was associated with better cognition (i.e., working-memory and linguistic-closure) and with more positive self-reported listening experiences, both in the laboratory and in daily life. We argue that listening efficiency, measured using the approach described here, is: (i) conceptually well-motivated, in that it is theoretically impervious to differences in how individuals approach the speed-accuracy trade-off that is inherent to all perceptual decision making; and (ii) of practical utility, in that it is sensitive to differences in task demand, and to differences between groups, even when speech intelligibility remains at or near ceiling level. Further research is needed to explore the sensitivity and practical utility of this metric across diverse listening situations.

A two-stages global sensitivity analysis by using the δ sensitivity index in presence of correlated inputs: application on a tumor growth inhibition model based on the dynamic energy budget theory

Global sensitivity analysis (GSA) evaluates the impact of variability and/or uncertainty of the model parameters on given model outputs. GSA is useful for assessing the quality of Pharmacometric model inference. Indeed, model parameters can be affected by high (estimation) uncertainty due to the sparsity of data. Independence between model parameters is a common assumption of GSA methods. However, ignoring (known) correlations between parameters may alter model predictions and, then, GSA results. To address this issue, a novel two-stages GSA technique based on the δ index, which is well-defined also in presence of correlated parameters, is here proposed. In the first step, statistical dependencies are neglected to identify parameters exerting causal effects. Correlations are introduced in the second step to consider the real distribution of the model output and investigate also the ‘indirect’ effects due to the correlation structure. The proposed two-stages GSA strategy was applied, as case study, to a preclinical tumor-in-host-growth inhibition model based on the Dynamic Energy Budget theory. The aim is to evaluate the impact of the model parameter estimate uncertainty (including correlations) on key model-derived metrics: the drug threshold concentration for tumor eradication, the tumor volume doubling time and a new index evaluating the drug efficacy-toxicity trade-off. This approach allowed to rank parameters according to their impact on the output, discerning whether a parameter mainly exerts a causal or ‘indirect’ effect. Thus, it was possible to identify uncertainties that should be necessarily reduced to obtain robust predictions for the outputs of interest.

Exploring Signature‐Based Model Calibration for Streamflow Prediction in Ungauged Basins

AbstractCalibration of precipitation‐streamflow models to streamflow signatures is a promising approach for streamflow prediction in ungauged basins (PUB). The estimation of parameter and prediction uncertainty in this case is not trivial because: (a) calibration takes place in the signature domain, while predictions are required in the time domain, and (b) streamflow signatures are estimated (e.g., from donor catchments) rather than “observed” (computed from observed streamflow in the target catchment), and therefore particularly uncertain. This study investigates model calibration using estimated signatures in an Approximate Bayesian Computation framework. First, we construct a stochastic signature transfer model, based on seasonal flow duration curves. Second, we calibrate a precipitation‐streamflow model to the estimated signatures, accounting for their uncertainty. The proposed method is tested in six catchments of the Thur basin, Switzerland. Three data availability scenarios are considered: (a) concomitant scenario, where signatures are “observed,” (b) non‐concomitant scenario, where signatures are transferred from a different time period, and (c) regionalization scenario, where signatures are transferred from (neighboring) donor catchments. In this study, the switch from observed to regionalized signatures increases predictive streamflow uncertainty by 38% and worsens the (deterministic) fit to observations by 17% (in terms of Nash‐Sutcliffe efficiency). Despite this deterioration, posterior predictive uncertainty remains lower than prior predictive uncertainty generated using uniform priors over representative parameter ranges (“uncalibrated” model), which demonstrates the effectiveness of the proposed signature‐based calibration. More importantly, uncertainty is reliably estimated at the ungauged catchments, which represents a key advance in stochastic streamflow PUB.

SUMRAY: R and Python Codes for Calculating Cancer Risk Due to Radiation Exposure of a Population

Background: Quantitative risk assessments should be accompanied by uncertainty analyses of the risk models employed in the calculations. In this study, we aim to develop a computational code named SUMRAY for use in cancer risk projections from radiation exposure taking into account uncertainties. We also aim to make SUMRAY publicly available as a resource for further improvement of risk projection.Materials and Methods: SUMRAY has two versions of code written in R and Python. The risk models used in SUMRAY for all-solid-cancer mortality and incidence were those published in the Life Span Study of a cohort of the atomic bomb survivors in Hiroshima and Nagasaki. The confidence intervals associated with the evaluated risks were derived by propagating the statistical uncertainties in the risk model parameter estimates by the Monte Carlo method.Results and Discussion: SUMRAY was used to calculate the lifetime or time-integrated attributable risks of cancer under an exposure scenario (baseline rates, dose[s], age[s] at exposure, age at the end of follow-up, sex) specified by the user. The results were compared with those calculated using another well-known web-based tool, Radiation Risk Assessment Tool (Rad- RAT; National Institutes of Health), and showed a reasonable agreement within the estimated confidential interval. Compared with RadRAT, SUMRAY can be used for a wide range of applications, as it allows the risk projection with arbitrarily specified risk models and/or population reference data.Conclusion: The reliabilities of SUMRAY with the present risk-model parameters and their variance-covariance matrices were verified by comparing them with those of the other codes. The SUMRAY code is distributed to the public as an open-source code under the Massachusetts Institute of Technology license.

Quantification of early nonpharmaceutical interventions aimed at slowing transmission of Coronavirus Disease 2019 in the Navajo Nation and surrounding states (Arizona, Colorado, New Mexico, and Utah).

During an early period of the Coronavirus Disease 2019 (COVID-19) pandemic, the Navajo Nation, much like New York City, experienced a relatively high rate of disease transmission. Yet, between January and October 2020, it experienced only a single period of growth in new COVID-19 cases, which ended when cases peaked in May 2020. The daily number of new cases slowly decayed in the summer of 2020 until late September 2020. In contrast, the surrounding states of Arizona, Colorado, New Mexico, and Utah all experienced at least two periods of growth in the same time frame, with second surges beginning in late May to early June. Here, we investigated these differences in disease transmission dynamics with the objective of quantifying the contributions of non-pharmaceutical interventions (NPIs) (e.g., behaviors that limit disease transmission). We considered a compartmental model accounting for distinct periods of NPIs to analyze the epidemic in each of the five regions. We used Bayesian inference to estimate region-specific model parameters from regional surveillance data (daily reports of new COVID-19 cases) and to quantify uncertainty in parameter estimates and model predictions. Our results suggest that NPIs in the Navajo Nation were sustained over the period of interest, whereas in the surrounding states, NPIs were relaxed, which allowed for subsequent surges in cases. Our region-specific model parameterizations allow us to quantify the impacts of NPIs on disease incidence in the regions of interest.